Related papers: Are almost-symmetries almost linear?
We first show that partial transposition for pure and mixed two-particle states in a discrete $N$-dimensional Hilbert space is equivalent to a change in sign of the momentum of one of the particles in the Wigner function for the state. We…
Conic quasi-linear maps are nonlinear operators from $C_0(X)$ to a normed linear space $E$ which preserve nonnegative linear combinations on positive cones generated by single functions; quasi-linear maps are linear on singly generated…
A state in a d-dimensional Hilbert space can be simulated by a state defined in a different dimension with high fidelity. We assess how faithfully such the approximated state can perform quantum protocols, using an example of the squeezed…
We introduce a smooth mapping of some discrete space-time symmetries into quasi-continuous ones. Such transformations are related with q-deformations of the dilations of the Euclidean space and with the non-commutative space. We work out…
We introduce a quasi-probability phase space distribution with two pairs of azimuthal-angular coordinates. This representation is well adapted to describe quantum systems with discrete symmetry. Quantum error correction of states encoded in…
When a $4D$ supersymmetric theory is placed on $S^3 \times \mathbb{R}$, the supersymmetric algebra is necessarily modified to $su(2|1)$ and we are dealing with a weak supersymmetric system. For such systems, the excited states of the…
Following Schmidt, Thurnheer and Bugeaud-Kristensen, we study how Dirichlet's theorem on linear forms needs to be modified when one requires that the vectors of coefficients of the linear forms make a bounded acute angle with respect to a…
Wigner and Husimi transforms have long been used for the phase-space reformulation of Schr\"odinger-type equations, and the study of the corresponding semiclassical limits. Most of the existing results provide approximations in appropriate…
Symmetries are defined in histories-based theories paying special attention to the class of history theories admitting quasitemporal structure (a generalization of the concept of `temporal sequences' of `events' using partial semigroups)…
Does quantum theory apply at all scales, including that of observers? New light on this fundamental question has recently been shed through a resurgence of interest in the long-standing Wigner's friend paradox. This is a thought experiment…
In this paper it is stressed that there is no {\em physical} reason for symmetries to be linear and that Lie group theory is therefore too restrictive. We illustrate this with some simple examples. Then we give a readable review on the…
The quantum mechanical transition probability is symmetric. A probabilistically motivated and more general quantum logical definition of the transition probability was introduced in two preceding papers without postulating its symmetry, but…
In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian fields. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems…
We consider a Wigner-type ensemble, i.e. large hermitian $N\times N$ random matrices $H=H^*$ with centered independent entries and with a general matrix of variances $S_{xy}=\mathbb E|H_{xy}|^2$. The norm of $H$ is asymptotically given by…
We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…
We isolate a geometric mechanism that complements the dynamical suppression of macroscopic interference: In a high-dimensional Hilbert space, almost all state vectors are nearly orthogonal, accommodating an exponentially large reservoir of…
We perform a minisuperspace analysis of an information-theoretic nonlinear Wheeler-deWitt (WDW) equation for de Sitter universes. The nonlinear WDW equation, which is in the form of a difference-differential equation, is transformed into a…
Let $H$ be a Hilbert space and $P(H)$ be the projective space of all quantum pure states. Wigner's theorem states that every bijection $\phi\colon P(H)\to P(H)$ that preserves the quantum angle between pure states is automatically induced…
The contribution of this work is twofold. The first part deals with a Hilbert-space version of McCann's celebrated result on the existence and uniqueness of monotone measure-preserving maps: given two probability measures $\rm P$ and $\rm…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…